Suppose that f: (a, b) → R is a differentiable function that is uniformly continuous. Is f' a bounded function? If yes, then provide a proof. If no, then give a counterexample.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 48E
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(7) Suppose that f: (a, b) → R is a differentiable function that is uniformly continuous. Is
f' a bounded function? If yes, then provide a proof. If no, then give a counterexample.
Transcribed Image Text:(7) Suppose that f: (a, b) → R is a differentiable function that is uniformly continuous. Is f' a bounded function? If yes, then provide a proof. If no, then give a counterexample.
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